16.1 Wavefunction analysis and Molecular Properties

Molecular properties (electrostatic moments, relativistic corrections, population analyses for densities and MOs, construction of localized MOs, etc.) can be calculated with the module moloch. Note that this program does not support unrestricted open-shell input (a script called moloch2 can currently be used as a work-around; type moloch2 -help for further information). Moreover, analyses of densities apart from those calculated from molecular orbitals (e.g. MP2 densities, densities of excited states) are not possible. For the current version of moloch we refer to the keywords listed in Section 20.2.20 which partly can also be set by define (see also Chapter 4).

Note: moloch is no longer supported, but

most functionalities of moloch now are integrated in programs that generate MOs or densities and can be done directly within the modules dscf, ridft, rimp2, mpgrad, ricc2 and egrad. If (some of) following keywords are set, corresponding operations will be performed in the end of these programs. If one desires to skip the MO- or density generating step, in case of programs dscf, ridft, rimp2 and mpgrad it is possible to directly jump to the routine performing analyses by typing "<program> -proper". Currently, the respective keywords have to be inserted in the control file by hand (not by define).

Here we briefly present the functionalities (i.e. the default use of keywords), non-default suboptions are described in detail in Section 20.2.21.

Electrostatic moments: up to quadrupole moments are calculated by default for the above modules.

Relativistic corrections: $mvd leads to calculation of relativistic corrections for the SCF total density in case of dscf and ridft, for the SCF+MP2 density in case of rimp2 and mpgrad and for that of the calculated excited state in case of egrad. Quantities calculated are expectation values < p2 >,< p4 > and the Darwin term ( 1∕ZA * ρ(RA)). Note, that at least the Darwin term requires an accurate description of the cusp in the wave function, thus the use of basis sets with uncontracted steep basis functions is recommended. Moreover note, that the results for these quantities are not too reasonable if ECPs are used (a respective warning is written to the output).

Population analyses: Population analyses are driven by the keyword $pop.

Without any extension Mulliken population analyses (MPA) are carried out for all densities present in the respective program, e.g. total (and spin) densities leading to Mulliken charges (and unpaired electrons) per atom in RHF(UHF)-type calculations in dscf or ridft, SCF+MP2 densities in rimp2 or mpgrad, excited state densities in egrad. Suboptions (see Section 20.2.21) also allow for calculation of Mulliken contributions of selectable atoms to selectable MOs including provision of data for graphical output (simulated density of states).

With $pop nbo a Natural Population Analysis (NPA) [154] is done. Currently only the resulting charges are calculated.

With $pop paboon a population analyses based on occupation numbers [155] is performed yielding "shared electron numbers (SENs)" and multicenter contributions. For this method always the total density is used, i.e. the sum of alpha and beta densities in case of UHF, the SCF+MP2-density in case of MP2 and the GHF total density for (two-component-)GHF. Note that the results of such an analysis may depend on the choice of the number of modified atomic orbitals ("MAOs"). By default, numbers of MAOs which are reasonable in most cases are taken (see Section 20.2.21). Nevertheless it is warmly recommended to carefully read the information concerning MAOs given in the output before looking at the numbers for atomic charges and shared electron numbers. For different ways of selecting MAOs see Section 20.2.21.

Generation of localized MOs: $localize enables calculation of localized molecular orbitals. Per default a Boys localization including all occupied MOs is carried out (i.e. the squared distance of charge centers of different LMOs is maximized). As output one gets localized MOs (written to files lmos or lalp /lbet in UHF cases), informations about dominant contributions of canonical MOs to LMOs and about location of LMOs (from Mulliken PA) are written to standard output.

Natural transition orbitals For excited states calculated at the CIS (or CCS) level the transition density between the ground and an excited state

Eia = Ψex|aia a|Ψex (16.1)
can be brought to a diagonal form through a singular value decomposition (SVD) of the excitation amplitudes Eia:
[OEV] ij = δij√ λ-i (16.2)
The columns of the matrices O and V belonging to a certain singular value λi can be interpreted as pairs of occupied and virtual natural transition orbitals [156,157] and the singular values λi are the weights with which this occupied-virtual pair contributes to the excitation. Usually electronic excitations are dominated by one or at least just a few NTO transitions and often the NTOs provide an easier understanding of transition than the excitation amplitudes Eia in the canonical molecular orbital basis.

From excitation amplitudes computed with the ricc2 program NTOs and their weights (the singular values) can be calculated with ricctools. E.g. using the right eigenvectors for the second singlett excited state in irrep 1:

ricctools -ntos CCRE0-2--1---1

The results for the occupied and virtual NTOs will be stored in files named, respectively, ntos_occ and ntos_vir. Note that the NTO analysis ignores for the correlated methods (CIS(D), ADC(2), CC2, CCSD, etc.) the double excitation contributions and correlation contributions to the ground state. This is no problem for single excitation dominated transition out of a “good” single reference ground state, in particular if only a qualitative picture is wanted, but one has to be aware of these omission when using NTOs for states with large double excitation contributions or when they are used for quantitative comparisons.

Fit of charges due to the electrostatic potential: $esp_fit fits point charges at the positions of nuclei to electrostatic potential arising from electric charge distribution (for UHF cases also for spin density, also possible in combination with $soghf). For this purpose the ("real") electrostatic potential is calculated at spherical shells of grid points around the atoms. By default, Bragg-Slater radii, rBS, are taken as shell radii.

A parametrization very close to that suggested by Kollman (a multiple-shell model with shells of radii ranging from 1.4*rvdW to 2.0*rvdW , rvdW is the van-der-Waals radius; U.C. Singh, P.A. Kollman, J. Comput. Chem. 5(2), 129-145 (1984)) is used if the keyword is extended:

$esp_fit kolman